针对二元函数满足强Wolfe条件的线搜索算法的MATLAB例程
时间: 2024-03-13 08:43:26 浏览: 16
以下是一个针对二元函数满足强Wolfe条件的线搜索算法的MATLAB例程,实现了Armijo条件、曲率条件以及强曲率条件的检查:
```matlab
function [alpha, num_evals] = strong_wolfe_search(f, g, x, p, alpha_init)
% Set the initial values of alpha and other constants
alpha = alpha_init;
c1 = 1e-4;
c2 = 0.9;
max_evals = 100;
num_evals = 0;
% Evaluate the objective function and its gradient at the starting point
f0 = f(x(1), x(2));
g0 = g(x(1), x(2));
% Initialize variables for the strong Wolfe conditions
alpha_lo = 0;
alpha_hi = Inf;
f_lo = f0;
g_lo = g0;
f_hi = f0;
g_hi = g0;
% Loop until the strong Wolfe conditions are satisfied or the maximum
% number of evaluations is reached
while num_evals < max_evals
% Evaluate the objective function and its gradient at the new point
f1 = f(x(1) + alpha*p(1), x(2) + alpha*p(2));
g1 = g(x(1) + alpha*p(1), x(2) + alpha*p(2));
% Check the Armijo condition
if f1 > f0 + c1*alpha*g0'*p
alpha_hi = alpha;
f_hi = f1;
g_hi = g1;
alpha = 0.5*(alpha_lo + alpha_hi);
else
% Check the curvature condition
if g1'*p < c2*g0'*p
alpha_lo = alpha;
f_lo = f1;
g_lo = g1;
alpha = 2*alpha_lo;
else
% Check the strong curvature condition
if g1'*p > -c2*g0'*p
alpha_hi = alpha;
f_hi = f1;
g_hi = g1;
alpha = 0.5*(alpha_lo + alpha_hi);
else
% If all conditions are satisfied, return the current alpha value
alpha_prev = alpha;
num_evals = num_evals + 1;
return;
end
end
end
% Update the number of function evaluations used
num_evals = num_evals + 1;
% If the maximum number of evaluations is reached, return the current alpha value
if num_evals == max_evals
alpha_prev = alpha;
fprintf('Maximum number of function evaluations reached\n');
return;
end
end
% Return the number of function evaluations used
if num_evals == max_evals
fprintf('Maximum number of function evaluations reached\n');
end
end
```
该例程采用了传统的回溯线搜索算法,并在此基础上添加了强曲率条件的检查。在每次迭代中计算一个新的alpha值,然后检查是否满足Armijo条件、曲率条件和强曲率条件。如果满足所有三个条件,则返回当前的alpha值。如果没有满足,则根据条件更新alpha值并继续迭代,直到达到最大迭代次数或满足条件为止。
请注意,此代码仅为演示目的。在实际应用中,您可能需要根据您的需求进行修改。